The last machine model of computation which we shall examine is the linear
bounded automaton or lba. These were originally developed as models for
actual computers rather than models for the computational process. They have
become important in the theory of computation even though they have not
emerged in applications to the extent which pushdown automata enjoy.
Here is the motivation for the design of this class of machines. Computers are
finite devices. They do not have unending amounts of storage like Turing
machines. Thus any actual computation done on a computer is not as extensive
as that which could be completed on a Turing machine. So, to mimic (or maybe
model) computers, we must restrict the storage capacity of Turing machines.
This should not be as severely as we did for finite automata though. Here is the
definition.